The number of segregating sites in a sample of DNA sequences from a geographically structured population

 The distribution of the number of segregating sites among randomly sampled DNA sequences from a geographically structured population is studied. We assume the infinitely-many-sites model of neutral genes and no recombination. Employing the genealogical process, we derive an equation for the generating function of the distribution of the number of segregating sites. First we study the strong-migration limit and prove that the distribution converges to that for a panmictic population. We also study the case of two sampled DNA sequences in the d-dimensional torus model with homogeneous migration. Received 13 July 1995; received in revised form 21 April 1997     

Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods

Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called the discrete gamma model, uses several categories of rates to approximate the gamma distribution, with equal probability for each category. The mean of each category is used to represent all the rates falling in the category. The performance of this method is found to be quite good, and four such categories appear to be sufficient to produce both an optimum, or near-optimum fit by the model to the data, and also an acceptable approximation to the continuous distribution. The second method, called fixed-rates model, classifies sites into several classes according to their rates predicted assuming the star tree. Sites in different classes are then assumed to be evolving at these fixed rates when other tree topologies are evaluated. Analyses of the data sets suggest that this method can produce reasonable results, but it seems to share some properties of a least-squares pairwise comparison; for example, interior branch lengths in nonbest trees are often found to be zero. The computational requirements of the two methods are comparable to that of Felsenstein's (1981, J Mol Evol 17:368–376) model, which assumes a single rate for all the sites.     

Maximum-likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites

Felsenstein's maximum-likelihood approach for inferring phylogeny from DNA sequences assumes that the rate of nucleotide substitution is constant over different nucleotide sites. This assumption is sometimes unrealistic, as has been revealed by analysis of real sequence data. In the present paper Felsenstein's method is extended to the case where substitution rates over sites are described by the gamma distribution. A numerical example is presented to show that the method fits the data better than do previous models.      

Second-order moments of segregating sites under variable population size

The identification of genomic regions that have been exposed to positive selection is a major challenge in population genetics. Since selective sweeps are expected to occur during environmental changes or when populations are colonizing a new habitat, statistical tests constructed on the assumption of constant population size are biased by the co-occurrence of population size changes and selection. To delimit this problem and gain better insights into demographic factors, theoretical results regarding the second-order moments of segregating sites, such as the variance of segregating sites, have been derived. Driven by emerging genomewide surveys, which allow the estimation of demographic parameters, a generalized version of Tajima's D has been derived that takes into account a previously estimated demographic scenario to test single loci for traces of selection against the null hypothesis of neutral evolution under variable population size.     

Recovery of crenarchaeotal ribosomal DNA sequences from freshwater-lake sediments.

We report several novel environmental sequences of archaea from the kingdom Crenarchaeota, recovered from anaerobic freshwater-lake sediments in Michigan. A nested PCR approach with Archaea- and Crenar-chaeota-specific primers was used to amplify partial Small-subunit ribosomal DNAs. Phylogenetic analysis of seven sequences shows that these DNAs represent a monophyletic lineage diverging prior to all recently identified crenarchaeotal phylotypes isolated from temperate environments. Including our lineage, all uncultured crenarchaeotal sequences recovered from moderate or cold environments form a distinct, monophyletic group separate from the "genuine" thermophilic crenarchaeota. Our finding extends the emerging picture that crenarchaeota, thought until recently to be solely extreme thermophiles, have radiated into an unexpectedly large variety of ecologically important, temperate environments.     

Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci

The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be approximately 20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.     

A new method for estimating effective population sizes from a single sample of multilocus genotypes

Equations for the effective size ( N_e ) of a population were derived in terms of the frequencies of a pair of offspring taken at random from the population being sibs sharing the same one or two parents. Based on these equations, a novel method (called sibship assignment method) was proposed to infer N_e from the sibship frequencies estimated from a sibship assignment analysis, using the multilocus genotypes of a sample of offspring taken at random from a single cohort in a population. Comparative analyses of extensive simulated data and some empirical data clearly demonstrated that the sibship assignment method is much more accurate [measured by the root mean squared error, RMSE, of 1/(2 N_e )] than other methods such as the heterozygote excess method, the linkage disequilibrium method, and the temporal method. The RMSE of 1/(2 N_e ) from the sibship assignment method is typically a small fraction of that from other methods. The new method is also more general and flexible than other methods. It can be applied to populations with nonoverlapping generations of both diploid and haplodiploid species under random or nonrandom mating, using either codominant or dominant markers. It can also be applied to the estimation of N_e for a subpopulation with immigration. With some modification, it could be applied to monoecious diploid populations with self-fertilization, and to populations with overlapping generations.     

Homozygosity in a population of variable size and mutation rate

A formula is obtained for the probability that two genes at a single locus, sampled at random from a population at time t, are of particular types. The model assumed is a diffusion approximation to a neutral Wright-Fisher model in which mutation is not necessarily symmetric and the population size is a function of time. It is shown that for symmetric mutation in a population undergoing a step-function type bottleneck, homozygosity increases with decreasing population size. A formula is given for the distribution of the number of segregating sites occurring in two randomly sampled sequences of completely linked sites, with general mutation at a site and identical mutation structure between sites.We give similar results for a population of fixed size but for which the mutation rate is a function of time, and not necessarily symmetric. We confirm the intuitively clear effect that increasing the mutation rate decreases homozygosity.     

Mutation accumulation in a selfing population: consequences of different mutation rates between selfers and outcrossers

Currently existing theories predict that because deleterious mutations accumulate at a higher rate, selfing populations suffer from more intense genetic degradation relative to outcrossing populations. This prediction may not always be true when we consider a potential difference in deleterious mutation rate between selfers and outcrossers. By analyzing the evolutionary stability of selfing and outcrossing in an infinite population, we found that the genome-wide deleterious mutation rate would be lower in selfing than in outcrossing organisms. When this difference in mutation rate was included in simulations, we found that in a small population, mutations accumulated more slowly under selfing rather than outcrossing. This result suggests that under frequent and intense bottlenecks, a selfing population may have a lower risk of genetic extinction than an outcrossing population.     

Adsorption of DNA to sand and variable degradation rates of adsorbed DNA.

Adsorption and desorption of DNA and degradation of adsorbed DNA by DNase I were studied by using a flowthrough system of sand-filled glass columns. Maximum adsorption at 23 degrees C occurred within 2 h. The amounts of DNA which adsorbed to sand increased with the salt concentration (0.1 to 4 M NaCl and 1 mM to 0.2 M MgCl2), salt valency (Na+ less than Mg2+ and Ca2+), and pH (5 to 9). Maximum desorption of DNA from sand (43 to 59%) was achieved when columns were eluted with NaPO4 and NaCl for 6 h or with EDTA for 1 h. DNA did not desorb in the presence of detergents. It is concluded that adsorption proceeded by physical and chemical (Mg2+ bridging) interaction between the DNA and sand surfaces. Degradability by DNase I decreased upon adsorption of transforming DNA. When DNA adsorbed in the presence of 50 mM MgCl2, the degradation rate was higher than when it adsorbed in the presence of 20 mM MgCl2. The sensitivity to degradation of DNA adsorbed to sand at 50 mM MgCl2 decreased when the columns were eluted with 0.1 mM MgCl2 or 100 mM EDTA before application of DNase I. This indicates that at least two types of DNA-sand complexes with different accessibilities of adsorbed DNA to DNase I existed. The degradability of DNA adsorbed to minor mineral fractions (feldspar and heavy minerals) of the sand differed from that of quartz-adsorbed DNA.     

Misalignment-mediated DNA polymerase beta mutations: comparison of microsatellite and frame-shift error rates using a forward mutation assay

Mutations arising in microsatellite DNA are associated with neurological diseases and cancer. To elucidate the molecular basis of microsatellite mutation, we have determined the in vitro polymerase error frequencies at microsatellite sequences representative of those found in the human genome: [GT/CA](10), [TC/AG](11), and [TTCC/AAGG](9). DNA templates contained the microsatellites inserted in-frame into the 5' region of the herpes simplex virus thymidine kinase (HSV-tk) gene. Polymerase beta (polbeta) error frequencies were quantitated in microsatellite sequences, relative to frame-shift error frequencies in coding sequences, from the same DNA synthesis reaction. The polbeta error frequencies within the dinucleotide sequences were (2-9) x 10(-3), 14-72-fold higher than the ssDNA template frequencies. The polbeta error frequencies within the tetranucleotide sequences were (4-6) x 10(-3), a 4-13-fold increase over background. Strand biases were observed for the [TC/AG](11) and [TTCC/AAGG](9) alleles, in which more errors were produced when the purine strand served as a template. Mutations within each microsatellite included noncanonical base substitution events and single nucleotide deletions as well as the expected unit length changes. An exponential relationship was observed between the polymerase error frequency per site and both the number of repetitive units and total length of the allele. Our observations are consistent with the strand slippage model of microsatellite mutagenesis and demonstrate that DNA sequence and/or structural differences result in mutational strand biases. To our knowledge, this is the first direct quantitation of DNA polymerase errors in vitro using template microsatellite sequences.     

Common and variable contributions of Fis residues to high-affinity binding at different DNA sequences

Fis is a nucleoid-associated protein that interacts with poorly related DNA sequences with a high degree of specificity. A difference of more than 3 orders of magnitude in apparent Kd values was observed between specific (Kd, approximately 1 to 4 nM) and nonspecific (Kd, approximately 4 microM) DNA binding. To examine the contributions of Fis residues to the high-affinity binding at different DNA sequences, 13 alanine substitutions were generated in or near the Fis helix-turn-helix DNA binding motif, and the resulting proteins were purified. In vitro binding assays at three different Fis sites (fis P II, hin distal, and lambda attR) revealed that R85, T87, R89, K90, and K91 played major roles in high-affinity DNA binding and that R85, T87, and K90 were consistently vital for binding to all three sites. Other residues made variable contributions to binding, depending on the binding site. N84 was required only for binding to the lambda attR Fis site, and the role of R89 was dramatically altered by the lambda attR DNA flanking sequence. The effects of Fis mutations on fis P II or hin distal site binding in vitro generally correlated with their abilities to mediate fis P repression or DNA inversion in vivo, demonstrating that the in vitro DNA-binding effects are relevant in vivo. The results suggest that while Fis is able to recognize a minimal common set of DNA sequence determinants at different binding sites, it is also equipped with a number of residues that contribute to the binding strength, some of which play variable roles.     

Recovery of YAC-end sequences through complementation of an Escherichia coli pyrF mutation.

We have developed a genetic means to recover sequences from YAC-ends near the yeast selectable marker URA3. This strategy is based on the ability of URA3 to complement mutations in pyrF, an Escherichia coli gene required for pyrimidine biosynthesis. We have developed an E.coli strain with a non-reverting allele of pyrF that is also suitable for cloning (recA-, hsdR-). We demonstrate the utility of this complementation strategy to obtain right-end clones from three YACs containing Arabidopsis thaliana DNA.     

Estimation of the ancestral effective population sizes of African great apes under different selection regimes

Reliable estimates of ancestral effective population sizes are necessary to unveil the population-level phenomena that shaped the phylogeny and molecular evolution of the African great apes. Although several methods have previously been applied to infer ancestral effective population sizes, an analysis of the influence of the selective regime on the estimates of ancestral demography has not been thoroughly conducted. In this study, three independent data sets under different selective regimes were used were composed to tackle this issue. The results showed that selection had a significant impact on the estimates of ancestral effective population sizes of the African great apes. The inference of the ancestral demography of African great apes was affected by the selection regime. The effects, however, were not homogeneous along the ancestral populations of great apes. The effective population size of the ancestor of humans and chimpanzees was more impacted by the selection regime when compared to the same parameter in the ancestor of humans, chimpanzees and gorillas. Because the selection regime influenced the estimates of ancestral effective population size, it is reasonable to assume that a portion of the discrepancy found in previous studies that inferred the ancestral effective population size may be attributable to the differential action of selection on the genes sampled.     

Estimation of hominoid ancestral population sizes under bayesian coalescent models incorporating mutation rate variation and sequencing errors

Estimation of population parameters for the common ancestors of humans and the great apes is important in understanding our evolutionary history. In particular, inference of population size for the human-chimpanzee common ancestor may shed light on the process by which the 2 species separated and on whether the human population experienced a severe size reduction in its early evolutionary history. In this study, the Bayesian method of ancestral inference of Rannala and Yang (2003. Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci. Genetics. 164:1645-1656) was extended to accommodate variable mutation rates among loci and random species-specific sequencing errors. The model was applied to analyze a genome-wide data set of approximately 15,000 neutral loci (7.4 Mb) aligned for human, chimpanzee, gorilla, orangutan, and macaque. We obtained robust and precise estimates for effective population sizes along the hominoid lineage extending back approximately 30 Myr to the cercopithecoid divergence. The results showed that ancestral populations were 5-10 times larger than modern humans along the entire hominoid lineage. The estimates were robust to the priors used and to model assumptions about recombination. The unusually low X chromosome divergence between human and chimpanzee could not be explained by variation in the male mutation bias or by current models of hybridization and introgression. Instead, our parameter estimates were consistent with a simple instantaneous process for human-chimpanzee speciation but showed a major reduction in X chromosome effective population size peculiar to the human-chimpanzee common ancestor, possibly due to selective sweeps on the X prior to separation of the 2 species.     

High spontaneous mutation frequency in shuttle vector sequences recovered from mammalian cellular DNA.

The recombinant shuttle vector pSV2gpt was introduced into V79 Chinese hamster cells, and stable transformants expressing the Escherichia coli gpt gene were selected. Two transformants carrying tandem duplications of the plasmid at a single site were identified and fused to simian COS-1 cells. Plasmid DNA recovered from the heterokaryons was used to transform a Gpt- derivative of E. coli HB101, and the relative frequency of plasmids carrying a mutation in the gpt gene was determined. The high frequency of Gpt- plasmids (ca. 1%) was similar to that observed when plasmid was recovered from COS-1 cells which had been transfected with pSV2gpt. Most of the mutant plasmids had rearrangements in the region containing the gpt gene.     

Expectation maximization algorithm for identifying protein-binding sites with variable lengths from unaligned DNA fragments.

An Expectation Maximization algorithm for identification of DNA binding sites is presented. The approach predicts the location of binding regions while allowing variable length spacers within the sites. In addition to predicting the most likely spacer length for a set of DNA fragments, the method identifies individual sites that differ in spacer size. No alignment of DNA sequences is necessary. The method is illustrated by application to 231 Escherichia coli DNA fragments known to contain promoters with variable spacings between their consensus regions. Maximum-likelihood tests of the differences between the spacing classes indicate that the consensus regions of the spacing classes are not distinct. Further tests suggest that several positions within the spacing region may contribute to promoter specificity.     

On the minimum number of topologies explaining a sample of DNA sequences

In this article I derive an alternative algorithm to Hudson and Kaplan's (Genetics 111, 147-165) algorithm that gives a lower bound to the number of recombination events in a sample's history. It is shown that the number, T(M), found by the algorithm is the least number of topologies required to explain a set of DNA sequences sampled under the infinite-site assumption. Let Tao = (T(1),...,T(r)) be a list of topologies compatible with the sequences, i.e., T(k) is compatible with an interval, I(k), of sites in the alignment. A characterization of all lists having T(M) topologies is given and it is shown that T(M) relates to specific patterns in the alignment, here called chain series. Further, a number of theorems relating general lists of topologies to the number T(M) is presented. The results are discussed in relation to the true minimum number of recombination events required to explain an alignment.     

Estimating mutation rate and generation time from longitudinal samples of DNA sequences

We present in this paper a simple method for estimating the mutation rate per site per year which also yields an estimate of the length of a generation when mutation rate per site per generation is known. The estimator, which takes advantage of DNA polymorphisms in longitudinal samples, is unbiased under a number of population models, including population structure and variable population size over time. We apply the new method to a longitudinal sample of DNA sequences of the env gene of human immunodeficiency virus type 1 (HIV-1) from a single patient and obtain 1.62 x 10(-2) as the mutation rate per site per year for HIV-1. Using an independent data set to estimate the mutation rate per generation, we obtain 1.8 days as the length of a generation of HIV-1, which agrees well with recent estimates based on viral load data. Our estimate of generation time differs considerably from a recent estimate by Rodrigo et al. when the same mutation rate per site per generation is used. Some factors that may contribute to the difference among different estimators are discussed.